Hamiltonian Truncation Study of the Phi^4 Theory in Two Dimensions II. The Z_2-Broken Phase and the Chang Duality

TL;DR

This paper advances the Fock-space Hamiltonian truncation method to analyze the Z_2-broken phase of two-dimensional Phi^4 theory, confirming the Chang duality through numerical checks and extending previous work on the symmetric phase.

Contribution

It introduces improved treatment of the scalar zero mode in Hamiltonian truncation and applies it to the Z_2-broken phase, providing new insights into duality and phase structure.

Findings

Validated the weak/strong duality numerically.

Extended Hamiltonian truncation to broken symmetry phase.

Provided detailed analysis of the zero mode treatment.

Abstract

The Fock-space Hamiltonian truncation method is developed further, paying particular attention to the treatment of the scalar field zero mode. This is applied to the two-dimensional Phi^4 theory in the phase where the Z_2-symmetry is spontaneously broken, complementing our earlier study of the Z_2-invariant phase and of the critical point. We also check numerically the weak/strong duality of this theory discussed long ago by Chang.